A Hall-effect sensor may be used to measure the charge-carrier density of a material that provides an electric current channel of a Hall-effect sensor. A constant electric current is passed along the electric current channel of the material in a longitudinal direction and a voltage is measured across the channel in a transverse direction. The voltage, known as the Hall voltage, is proportional to the vector cross product of the electric current and any local magnetic field divided by the charge-carrier density.
It can be difficult to create a sensitive charge-carrier Hall-effect sensor.
In order to detect a small change in the charge-carrier density by measuring a change in the Hall voltage, a vector cross product of the magnetic field and the current needs to be sufficiently high and the charge-carrier density needs to be sufficiently low and homogeneous across the sample.